The housing problem and revealed preference theory: duality and an application

TL;DR

This paper reveals a duality between Afriat's revealed preference theory and the Shapley-Scarf housing allocation problem, providing new insights and indices for data rationalizability.

Contribution

It establishes a duality linking revealed preference theory with housing allocation, offering a geometric characterization and new rationalizability indices.

Findings

Afriat's theorem as a second welfare theorem in housing

Connection of revealed preference to an optimal assignment problem

Introduction of new indices and weaker notions of rationalizability

Abstract

This paper exhibits a duality between the theory of Revealed Preference of Afriat and the housing allocation problem of Shapley and Scarf. In particular, it is shown that Afriat's theorem can be interpreted as a second welfare theorem in the housing problem. Using this duality, the revealed preference problem is connected to an optimal assignment problem, and a geometrical characterization of the rationalizability of experiment data is given. This allows in turn to give new indices of rationalizability of the data, and to define weaker notions of rationalizability, in the spirit of Afriat's efficiency index.